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  • 1
    Electronic Resource
    Electronic Resource
    On the Composition of the Solar Interior Rapporteur Paper I (1998)
    Springer
    Space science reviews 85 (1998), S. 141-158 
    Details
    ISSN: 1572-9672
    Keywords: equation of state ; opacity ; helium abundance ; lithium abundance ; tachocline ; solar neutrinos ; helioseismology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Standard solar models, although they are free from the influence of much of the fluid motion that is bound to be present in the Sun, have been shown by helioseismology to represent the spherically averaged structure of the Sun amazingly well. This state of affairs has come about after painstaking refinements by a great many people of the pertinent microphysics, including that which controls the equation of state, the opacity, the nuclear reaction rates and the diffusion that inhibits gravitational segregation of chemical elements. It has instilled confidence in the modellers in being able to predict the composition of the solar interior. But there are consequences of the flow, related particularly to redistribution of chemical species, that can be difficult to identify observationally, yet which may degrade any inferences we might make. Their potential presence must at least be acknowledged by anyone who tries to asses the reliability of the models. This report summarizes the discussions in the preceding pages of this volume of the current theoretical and observational status of the subject, pointing to many of the caveats that have been raised, and attempting at the same time to put them into a seemingly coherent discourse in the context of our present understanding of the workings of the solar interior.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005105224272
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  • 2
    Electronic Resource
    Electronic Resource
    Application of the thermodynamics of curved boundary layers to the scaled particle theory of hard-sphere fluids (1973)
    Springer
    Journal of statistical physics 8 (1973), S. 299-307 
    Details
    ISSN: 1572-9613
    Keywords: Statistical thermodynamics of curved boundary layers ; scaled particle theory ; equation of state ; cycle equation ; fluid-solid phase transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The thermodynamics of curved boundary layers, with the assumption that the distance between the surface of a fluid cavity and its surface of tension is a quadratic function of the cavity radius, is applied to the exact thermo-dynamic expression forG, the central function of scaled particle theory. The coefficients in the quadratic representation are determined so as to satisfyall five of the known exact conditions onG valid for cavity radii between one-half and one molecular diameter. The results of the calculation are displayed as the hard-sphere equation of state, the boundary tension associated with the surface of tension, and the distance between the cavity surface and the surface of tension. Although the hard-sphere equation of state obtained by this method using all five conditions onG is more accurate than in the case where only two or three conditions are used, the original scaled particle theory, in whichG itself was represented simply by a quadratic function of inverse powers of cavity radius, still yields the more accurate equation of state. Nevertheless, the present approach limits approximations to the distance between the cavity surface and the surface of tension, a small quantity in itself. The path to a still more improved theory remains well defined, contingent upon the discovery of additional exact conditions, and does not depend, as in the original scaled particle theory, on a form forG arrived at in a somewhat ad hoc manner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020269
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  • 3
    Electronic Resource
    Electronic Resource
    A general approach to association using cluster partition functions (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 1287-1306 
    Details
    ISSN: 1572-9613
    Keywords: Association ; phase equilibrium ; statistical mechanics ; partition function ; chemical engineering ; equation of state ; chemical equilibrium ; cluster distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A systematic and fundamental approach to associating mixtures is presented. It is shown how the thermodynamic functions may be computed starting from a partition function based on the cluster concept such as occurs in chemical theory. The theory provides a basis for and an extension of the existing chemical theory of (continuous) association. It is applicable to arbitrary association schemes. Analysis of separate cases is not necessary. The assumptions that were made to allow the development were chosen such as to make the principle of reactivity valid. It is this same principle that links various theories: the chemical theory of continuous association, the lattice fluid hydrogen bonding model, and first-order perturbation theory. The equivalence between these theories in appropriate limits is shown in a general and rigorous way. The theory is believed to provide a practical framework for engineering modeling work. Binary interaction parameters can be incorporated. The association scheme is accounted for by a set of generic equations, which should facilitate robust implementation in computer programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02181285
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  • 4
    Electronic Resource
    Electronic Resource
    Performance of the complete travel-time equation of state at simultaneous high pressure and temperature (1993)
    Springer
    Pure and applied geophysics 141 (1993), S. 379-392 
    Details
    ISSN: 1420-9136
    Keywords: Elastic constant ; thermodynamics ; equation of state ; acoustic velocity ; thermal expansivity ; heat capacity ; Grüneisen constant ; high pressure ; high temperature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The complete travel-time equation of state (CT-EOS) is presented by utilizing thermodynamics relations, such as; $$K_T = K_S (1 + \alpha \gamma T)^{ - 1} , \gamma = \frac{{\alpha K_S }}{{\rho C_P }}, \left. {\frac{{\partial C_P }}{{\partial P}}} \right)_T = - \frac{T}{\rho }\left[ {\alpha ^2 + \left. {\frac{{\partial \alpha }}{{\partial T}}} \right)_P } \right], etc.$$ The CT-EOS enables us to analyze ultrasonic experimental data under simultaneous high pressure and high temperature without introducing any assumption, as long as the density, or thermal expansivity, and heat capacity are also available as functions of temperature at zero pressure. The performance of the CT-EOS was examined by using synthesized travel-time data with random noise of 10−5 and 10−4 amplitude up to 4 GPa and 1500 K. Those test conditions are to be met with the newly developed GHz interferometry in a gas medium piston cylinder apparatus. The results suggest that the combination of the CT-EOS and accurate experimental data (10−4 in travel time) can determine thermodynamic and elastic parameters, as well as their derivatives with unprecedented accuracy, yielding second-order pressure derivatives (∂2 M/∂P 2) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivatives ∂2 M/∂P∂T). The completeness of the CT-EOS provides an unambiguous criterion to evaluate the compatibility of empirical EOS with experimental data. Furthermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i.e., volume) measurements are made simultaneously with the travel-time measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00998336
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  • 5
    Electronic Resource
    Electronic Resource
    Hydrothermal studies in a new diamond anvil cell up to 10 GPa and from −190°C to 1200°C (1993)
    Springer
    Pure and applied geophysics 141 (1993), S. 487-495 
    Details
    ISSN: 1420-9136
    Keywords: Pressure ; temperature ; hydrothermal ; H2O ; equation of state ; diamond anvil cell
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The new hydrothermal diamond anvil cell (HDAC) has been designed for optical microscopy and X-ray diffraction at pressures up to 10 GPa and temperatures between −190°C and 1200°C. Laser light reffected from the top and bottom anvil faces and the top and bottom solid sample faces produce interference fringes that provide a very sensitive means of monitoring the volume of sample chamber and for observing volume and refractive index changes in solid samples due to transitions and reactions. Synchrotron radiation has been used to make X-ray diffraction patterns of samples under hydrothermal conditions. Individual heaters and individual thermocouples provide temperature control with an accuracy of ±0.5°C. Liquid nitrogen directly introduced into the HDAC has been used to reduce the sample temperature to −190°C. The α-β phase boundary of quartz has been used to calculate the transition pressures from measured transition temperatures. With this method we have redetermined 5 isochores of H2O up to 850°C and 1.2 GPa at which the solution rate of the quartz became so rapid that the quartz dissolved completely before the α-β transition could be observed. When silica solutions were cooled, opal spherules and rods formed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00998341
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  • 6
    Electronic Resource
    Electronic Resource
    Accuracy in measurements and the temperature and volume dependence of thermoelastic parameters (1993)
    Springer
    Pure and applied geophysics 141 (1993), S. 327-339 
    Details
    ISSN: 1420-9136
    Keywords: Elasticity ; thermoelasticity ; piston-cylinder ; rectangular parallepiped resonance ; MgO ; NaCl ; Anderson-Grüneisen parameter ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract To obtain the temperatureT and volumeV (or pressureP) dependence of the Anderson-Grüneisen parameter δ T , measurements with high sensitivity are required. We show two examples:P, V, T measurements of NaCl done with the piston cylinder and elasticity measurements of MgO using a resonance method. In both cases, the sensitivity of the measurements leads to results that provide information about δ T (η,T), where η≡V/V 0 andV 0 is the volume at zero pressure. We demonstrate that determination of δ T leads to understanding of the volume and temperature dependence ofq=(∂ ln γ/∂ lnV) T over a broadV, T range, where γ is the Grüneisen ratio.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00998334
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  • 7
    Electronic Resource
    Electronic Resource
    A new ultrasonic interferometer for the determination of equation of state parameters of sub-millimeter single crystals (1993)
    Springer
    Pure and applied geophysics 141 (1993), S. 341-377 
    Details
    ISSN: 1420-9136
    Keywords: GHz ultrasonic interferometry ; diffraction ; acoustic wave ; bond effect ; equation of state ; elastic constant ; acoustic velocity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A new giga-Hertz ultrasonic interferometer has been developed, based on ultrasonic microscopy technology. The interferometer operates from 0.3 GHz to 1.5 GHz. The high frequency and associated small wavelengths together with the large bandwidth make it possible to measure travel times in samples with thicknesses of several microns and allow for unprecedented accuracy in bond corrections. An absolute accuracy of 1 part in 105 in travel time measurements is achievable in single crystals (thickness of ∼200 microns) or glasses of interest to the earth sciences. The high precision travel time data, combining with sample length measurements using a laser interferometer built in our laboratory, yield very high precision ultrasonic velocities. The interferometer is intended for use in conjunction with a newly developed 4 GPa gas piston cylinder apparatus (Getting andSpetzler, 1993) for equation of state measurements under simultaneous pressure and temperature. A separate correction for the bond will be made for each datum at every point in temperature pressure space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00998335
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  • 8
    Electronic Resource
    Electronic Resource
    Room-temperature compressibilities of MnO and CdO: further examination of the role of cation type in bulk modulus systematics (1999)
    Springer
    Physics and chemistry of minerals 26 (1999), S. 644-648 
    Details
    ISSN: 1432-2021
    Keywords: Key words MnO ; CdO ; rock-salt monoxides ; X-ray diffraction ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Room-temperature volume measurements up to 8.1 GPa reveal that rock-salt structured MnO and CdO have identical compressibility in the pressure range studied. In the plot of bulk modulus vs unit-cell volume, CdO plots well above the trend of the 3d transition metal monoxides, a behavior that deviates from empirical predictions of constant K 0 V 0. The present observations are in favor of our earlier suggestion that, for isostructural solids, the empirically predicted bulk modulus-volume relationship may be limited to their subsets that share the same valence electron character (i.e., s vs 3d vs 4d). For cations forming transition metal monoxides, variations of Pauling electronegativity with ionic radius show differences that are qualitatively similar to the observed trends of bulk modulus, suggesting that bond covalency differences may contribute to the different behaviors between the 3d and 4d transition metal monoxides.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002690050229
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  • 9
    Electronic Resource
    Electronic Resource
    Microphysics: Equation of State (1998)
    Springer
    Space science reviews 85 (1998), S. 49-60 
    Details
    ISSN: 1572-9672
    Keywords: helioseismology ; equation of state ; helium abundance ; excited states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The equation of state is one of the three fundamental ingredients used to construct stellar models. The plasma of the interiors of stars such as the Sun is only slightly non-ideal. However, the extraordinary accuracy of the helioseismological data requires refined equations of state. It turned out to be necessary to include a Coulomb correction, commonly evaluated in the Debye-Hückel approximation. Higher-order non-ideal effects have implications as well, both for plasma physics and for solar physics. As a typical example, the recently studied thermodynamic consequence of excited states in compound particles is discussed. This effect is of considerable relevance in the helioseismic determination of the helium abundance in the solar convection zone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005176317912
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  • 10
    Electronic Resource
    Electronic Resource
    Exact equations of state for one-dimensional chain fluids (1990)
    Springer
    Journal of statistical physics 61 (1990), S. 803-842 
    Details
    ISSN: 1572-9613
    Keywords: Chain molecule ; equation of state ; one dimension ; isothermal-isobaric ensemble
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using the isothermal-isobaric ensemble, exact equations of state are derived for three classical models of one-dimensional chain fluids. Each chain molecule is modeled by a series of linked sites which interact through nearest-neighbor bond potentials. In two of the models, the intramolecular bonds are modeled by infinitely deep square-well potentials, while in the third, the bonds are modeled by a harmonic potential. Intermolecular interactions are modeled by a hard-rod potential. Numerical results are presented for dimer and 8-mer fluids which illustrate the influence of chain length, well width and spring constant on the compressibility factor. The effect of adding an infinitely weak, infinitely long-ranged attractive interaction between the sites is also considered. The attractive tail induces a first-order phase transition of the gas-liquid type in all of the chain models. For certain values of the model parameters, however, two of the models show evidence of a second gas-liquid type transition, which appears to be associated with chain collapse.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01027302
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  • 11
    Electronic Resource
    Electronic Resource
    Further application of the statistical thermodynamics of curved surfaces to scaled particle theory (1973)
    Springer
    Journal of statistical physics 7 (1973), S. 143-159 
    Details
    ISSN: 1572-9613
    Keywords: Statistical thermodynamics of curved boundary layers ; scaledparticle theory ; equation of state ; cycle equation ; fluid-solid phase transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The thermodynamics of curved boundary layers is combined with scaled particle theory to determine the rigid-sphere equation of state. In particular, the boundary analog of the Gibbs-Tolman-Koenig-Buff equation is solved for a rigid-sphere fluid, using the approximation that the distance between the surface of a cavity and its surface of tension is a function of the density only (the first-order approximation). This, in conjunction with several exact conditions onG, the central function of scaled particle theory, leads to an approximate rigid-sphere fluid equation of state and a qualitatively correct rigid-sphere solid equation of state. The fluid isotherm compares favorably with previous results (2.9 % error in the fourth virial coefficient), but due to the inaccuracy of the solid isotherm, no phase transition is obtained. The theory described here is to be contrasted with previous approaches in that a less arbitrary functional form forG is assumed, and the surface of tension and cavity surface are not assumed to be coincident. The “cycle equation” of Reiss and Tully-Smith is rederived by a simpler route and shown to be correct to all orders of cavity curvature, rather than only first order as was originally thought. A new exact condition, obtained from the compressibility equation of state, is used as a boundary condition for the “cycle equation” to determine the location of the equimolecular surface. This molecular calculation compares favorably (discrepancy of 〈2 %) with a thermodynamic calculation based on the boundary analog of the Gibbs adsorption equation and indicates the accuracy and consistency of the first-order approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01024212
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  • 12
    Electronic Resource
    Electronic Resource
    Coulomb Systems at Low Density: A Review (1999)
    Springer
    Journal of statistical physics 96 (1999), S. 1163-1330 
    Details
    ISSN: 1572-9613
    Keywords: Coulomb ; plasma ; Saha ; screening ; Debye–Hückel ; virial ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Results on the correlations of low-density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system, Debye–Hückel screening, is compared and contrasted with the quantum case, where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye–Hückel screening is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004600603161
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  • 13
    Electronic Resource
    Electronic Resource
    High-density properties of hard spheres within a modified Percus-Yevick theory: The role of thermodynamic consistency (1991)
    Springer
    Journal of statistical physics 63 (1991), S. 141-165 
    Details
    ISSN: 1572-9613
    Keywords: Hard spheres ; tail function ; zero-separation theorems ; self-consistent theory ; equation of state ; random close packing ; closest packing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using an integral-equation approach based upon an approximation for the tail function, the equilibrium properties of a system of hard spheres are studied with special concern for the behavior in the region of close packing. The closure adopted is such that full, internal consistency is ensured in the thermodynamics of the model with respect to both the two zero-separation theorems as well as to the more standard virial and fluctuation routes to the equation of state. The scheme also makes use of the continuity properties of the tail function and of the cavity distribution function at contact. These properties are explictly tested in the low-density limit up to the fourth derivative. The theory generates an equilibrium branch bounded on the high-density side by a point corresponding to a packing fractionη≃0.78, a value which closely matches Rogers' least upper bound for the densest packing of spheres. The pair structure of the fluid in the state of random close packing is also compared to the type of local order predicted by the theory at similar densities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01026597
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  • 14
    Electronic Resource
    Electronic Resource
    Oscillation of the radial distribution function (1992)
    Springer
    Journal of statistical physics 68 (1992), S. 1065-1087 
    Details
    ISSN: 1572-9613
    Keywords: Nonnegative operator ; hard-sphere model ; radial distribution function ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We prove that the radial distribution function oscillates at low density in a system with a short-range nonnegative potential and investigate the branching of the solutions of an approximate equation of state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048885
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  • 15
    Electronic Resource
    Electronic Resource
    A thermodynamic property formulation for air. I. Single-phase equation of state from 60 to 873 K at pressures to 70 MPa (1990)
    Springer
    International journal of thermophysics 11 (1990), S. 169-177 
    Details
    ISSN: 1572-9567
    Keywords: air ; density ; equation of state ; fundamental equation ; heat capacity ; thermodynamic properties ; velocity of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A revised interim formulation for the thermodynamic properties of air has been developed for calculating properties of the vapor and estimating properties for the liquid at temperatures as low as 60 K. The formulation incorporates separate equations for the calculation of bubble-point and dew-point pressures and densities and for the ideal-gas heat capacity. A new fundamental equation of state is given for vapor and liquid states of air based upon available experimental data and predicted values of isochoric heat capacity for the liquid using corresponding states methods. Procedures for predicting C v are discussed. The fundamental equation for air is explicit in nondimensional Helmholtz energy. The terms of the fundamental equation were selected from a larger set of 75 proposed terms using a least-squares fitting procedure. Representative graphical comparisons of calculated property values to experimental measurements are given. The estimated accuracy of calculated densities is generally ± 0.2% except near the dew and bubble lines. Calculated heat capacities for the liquid must be considered only as estimates until substantiated by experimental measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00503868
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  • 16
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    Electronic Resource
    On the calculation of second virial coefficients for nonspherical molecules (1990)
    Springer
    International journal of thermophysics 11 (1990), S. 503-513 
    Details
    ISSN: 1572-9567
    Keywords: equation of state ; molecular gases ; nonspherical interactions ; second virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A self-consistent scheme is given for the calculation of the contributions of nonspherical molecular interactions to second virial coefficients. The usual longrange nonspherical interactions, which are asymptotically valid only at large separations, are modified by damping functions that render them valid at small separations as well. Numerical tables of new auxiliary functions J n D (T*) are given for 6⩽n⩽30 and 0.5⩽T *⩽10. These are designed to be used in the identical statistical-mechanical formalism for the second virial coefficient that had been developed for the undamped long-range nonspherical interactions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00500842
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  • 17
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    A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region (1991)
    Springer
    International journal of thermophysics 12 (1991), S. 549-562 
    Details
    ISSN: 1572-9567
    Keywords: critical parameters ; critical phenomena ; equation of state ; methane, ethane ; n-alkanes ; specific heat ; sound velocity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH4) to n-nonane (C9H20) in the critical region. The equation is valid in the reduced density range 0.7⩽ρ c⩽1.3 at T=T c and up to 1.2T c at ρ=ρ c.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00502368
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  • 18
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    Equation-of-state calculations of chemical reaction equilibrium in nonideal systems (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 199-213 
    Details
    ISSN: 1572-9567
    Keywords: chemical-reaction equilibria ; equation of state ; phase equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In order to calculate accurately chemical-reaction equilibria of a system over a wide range of temperatures and pressures, one must account for the non-idealities of the system. In this work, a method is developed to predict accurately chemical-reaction equilibria and phase equilibria of a system using an equation of state to account for the nonidealities. The general formalism for a multicomponent system with multiple reactions is presented. Three widely used cubic equations of state are used to calculate the physical properties of the species. The proposed method is applied to the water-gas shift reaction, to the decomposition of methylcyclohexane, and to the reaction of carbon monoxide with hydrogen sulfide over a wide range of temperatures and pressures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00507808
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  • 19
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    Special Equations of State for Methane, Argon, and Nitrogen for the Temperature Range from 270 to 350 K at Pressures up to 30 MPa (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 699-725 
    Details
    ISSN: 1572-9567
    Keywords: argon ; caloric properties ; density ; equation of state ; Helmholtz function ; methane ; nitrogen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In order to describe the thermodynamic behavior of methane, argon, and nitrogen in the so-called “natural-gas region,” namely, from 270 to 350 K at pressures up to 30 MPa as accurate as possible with equations of a very simple form, new equations of state for these three substances have been developed. These equations are in the form of a fundamental equation in the dimensionless Helmholtz energy; for calculating the pressure or the density, the corresponding equations explicit in pressure are also given. The residual parts of the Helmholtz function representing the behavior of the real gas contain 12 fitted coefficients for methane, 8 for argon, and 7 for nitrogen. The thermodynamic relations between the Helmholtz energy and the most important thermodynamic properties and the needed derivatives of the equations are explicitly given; to assist the user there is also a table with values for computer-program verification. The uncertainties when calculating the density ρ, the speed of sound w, the isobaric specific heat capacity c p, and the isochoric specific heat capacity c v are estimated as follows. For all three substances it is Δρ/ρ≤±0.02 % for p≤ 12 MPa and Δρ/ρ ≤ ±0.05% for higher pressures. For methane it is Δw/w≤±0.02% for p≤10 MPa and Δw/w≤+-0.1% for higher pressures; for argon it is Δw/w≲-0.1 % for p≤ 7 MPa, Δw/w≤±0.3 % for 7 〈p≤30 MPa; and for nitrogen it is Δw/w≤±0.1% for p≤1.5 MPa and Δw/w±0.5% for higher pressures. For all three substances it is Δc p/c p≤±1 % and ΔC v/C v≤±1 % in the entire range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00502103
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  • 20
    Electronic Resource
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    Equation of state for compressed liquids and their mixtures from the cohesive energy density (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 685-697 
    Details
    ISSN: 1572-9567
    Keywords: cohesive energy ; compressed liquids and mixtures ; equation of state ; statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A procedure is presented, based on statistical-mechanical theory, for predicting the equation of state of compressed normal liquids and their mixtures from two scaling constants that are available from measurements at ordinary pressures and temperatures. The theoretical equation of state is that of Ihm, Song, and Mason, and the two constants are the enthalpy of vaporization and the liquid density at the triple point, which are related to the cohesive energy density of regular solution theory. The procedure is tested on a number of substances ranging in complexity from Ar and CO2 to n-heptane and toluene. The results indicate that the liquid density at any pressure and temperature can be predicted within about 5%, over the range from T tp to T c and up to the freezing line. Possible methods of determining the scaling constants are discussed, as well as other possible choices for scaling constants.
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    An equation of state for pure fluids describing the critical region (1994)
    Springer
    International journal of thermophysics 15 (1994), S. 261-281 
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    ISSN: 1572-9567
    Keywords: critical behavior ; equation of state ; fluctuations
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    Notes: Abstract Density fluctuations of a pure nuid are treated by a cell model, in which the fluid is divided into cells containing different numbers of particles. A probability function for the particle number is derived. This function, after convolution with a classical (mean field) equation of state, leads to an improved equation of state which is valid in the critical region. The equation of state is analytical, hence not exact in the immediate vicinity of the critical point. As an example, the convolution is applied to the Carnahan-Starling/van der Waals equation of state; the resulting equation of state is used to correlate thermodynamic properties of several simple fluids.
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    URL: http://dx.doi.org/10.1007/BF01441586
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    Padé approximants applied to the equation of state and heat capacity of quantum ideal gases (1994)
    Springer
    International journal of thermophysics 15 (1994), S. 921-932 
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    ISSN: 1572-9567
    Keywords: Bose and Fermi quantum ideal gases ; equation of state ; heat ; capacity ; Padé approximants
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    Topics: Physics
    Notes: Abstract Padé approximants have been applied to the equation of state and heat capacity of the quantum ideal gases. For the Bose gas the agreement is almost perfect. For the Fermi gas, the maximum relative error is 0.03% for the former and 0.4% for the latter.
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    URL: http://dx.doi.org/10.1007/BF01447102
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    A corresponding-states principle for the equation of state of hard-convex-body fluids (1994)
    Springer
    International journal of thermophysics 15 (1994), S. 933-940 
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    ISSN: 1572-9567
    Keywords: equation of state ; corresponding states ; hard-convex-body fluids ; hard spheres
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    Topics: Physics
    Notes: Abstract A theoretically based corresponding-states principle is developed for the equation of state of hard-convex-body fluids. For all the fluids considered, the excess compressibility factor, reduced by means of a parameter which can be determined analytically. lies on a single curve whose analytical expression can be obtained from the equation of state of the hard-sphere fluid.
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    URL: http://dx.doi.org/10.1007/BF01447103
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    Application of a new selection algorithm to the development of a wide-range equation of state for refrigerant R134a (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 101-110 
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    ISSN: 1572-9567
    Keywords: equation of state ; R 134a ; refrigerants ; simulated annealing ; stepwise regression ; thermodynamic properties
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    Topics: Physics
    Notes: Abstract Refrigerant R134a (1,1.1,2-tetrafuoroethane) is a leading substitute for refrigerant R12. As such, there has been worldwide activity to develop accurate wide-range equations of state for this fluid. In this study. we have developed a new selection algorithm for determining high-accuracy equations of state in the Helmholtz representation. This method combines least-squares regression analysis with simulated annealing optimization. Simulated annealing, unlike stepwise regression, allows for the controlled acceptance of random increases in the objective function. Thus, this procedure produces a computationally efficient selection algorithm which is not susceptible to the function-space local-minima problems present in a purely stepwise regression approach. Two equations are presented in this work and compared against experimental data and other high-accuracy equations of state for R134a. One equation was produced strictly by using stepwise a regression algorithm, while the other was produced using the simulated-annealing selection algorithm. In both cases the temperature dependence of the equations was restricted to have no terms whose exponents were greater than live.
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    URL: http://dx.doi.org/10.1007/BF01438961
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    Equations of state for the thermodynamic properties of R32 (difluoromethane) and R125 (pentafluoroethane) (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 79-89 
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    ISSN: 1572-9567
    Keywords: difluoromethane (R32) ; equation of state ; pentafluoroethane (R125) ; thermodynamic properties
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    Topics: Physics
    Notes: Abstract Thermodynamic properties of difluoromethane (R32) and pentafluoroethane (R125) are expressed in terms of 32-term modified Benedict-Webb-Rubin (MBWR) equations of state. For each refrigerant, coefficients are reported for the MBWR equation and for ancillary equations used to fit the ideal-gas heat capacity and the coexisting densities and pressure along the saturation boundary. The MBWR coefficients were determined with a multiproperty fit that used the following types of experimental data: PVT: isochoric, isobaric, and saturated-liquid heal capacities; second virial coefficients; and properties at coexistence. The respective equations of stale accurately represent experimental data from 160 to 393 K and pressures to 35 MPa for R32 and from 174 to 448 K and pressures to 68 MPa for R125 with the exception of the critical regions. Both equations give reasonable results upon extrapolation to 500 K and 60 MPa. Comparisons between predicted and experimental values are presented.
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    A fundamental equation of state for 1,1-difluoroethane (HFC-152a) (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 91-100 
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    ISSN: 1572-9567
    Keywords: equation of state ; Helmholtz free energy ; HFC-152a ; refrigeranis
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    Topics: Physics
    Notes: Abstract A fundamental equation ofstale for HFC-152a ( 1,1-dilluorocthane) is presented covering temperatures between the triple-point temperature ( 154.56 K) and 435 K for pressures up to 311 M Pa. The equation is based on reliable (p, g, T) data in the range mentioned above. These are generally represented within ±0.1 % of density. Furthermore. experimental values of the vapor pressure, the saturated liquid density, and some isobaric heat capacities in the liquid were included during the correlation process. The new equation of state is compared with experimental data and also with the equation of state developed by Tamatsu et al. Differences between the two equations of state generally result from using different experimental input data. It is shown that the new equation of state allows an accurate calculation of various thermodynamic properties for most technical applications.
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    Determination of thermodynamic properties from the speed of sound (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 663-673 
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    ISSN: 1572-9567
    Keywords: equation of state ; speed of sound ; thermodynamic properties
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    Topics: Physics
    Notes: Abstract We describe methods by which all of the observable thermodynamic properties of a compressed gas, including the compressibility factor and the isochoric heat capacity, may be determined from sound speed data by numerical integration of a pair of partial differential equations. The technique may be employed over a wide range of conditions. Initial values are required. but we demonstrate that values specified on an isotherm close to the critical temperature are sufficient for application of the method to the entire homogeneous fluid region at subcritical densities. The method may also be extended to higher densities at temperatures above the critical. The effects of errors in both the initial values and the speed of sound are examined in detail by means of analytic and numerical results. The results indicate that all of the observable thermodynamic properties may be obtained with an uncertainty equal to or less than that achievable by the best available alternative techniques.
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    Molecular simulation and theory of associating chain molecules (1995)
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    International journal of thermophysics 16 (1995), S. 705-713 
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    ISSN: 1572-9567
    Keywords: associating fluids ; chain fluids ; computer simulations ; equation of state ; hydrogen bonding ; Lennard-Jones ; Monte Carlo
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    Topics: Physics
    Notes: Abstract A closed-form statistical mechanical based equation of state for associating chain fluids is presented. A Lennard-Jones chain is used as a reference to account for the repulsive, dispersive and anisotropic (size) contributions, while the short-range directional attraction is treated as a perturbation expansion based on Wertheim's first-order theory of associating fluids. A model fluid composed of a chain of tangently bonded Lennard-Jones spheres with an associating square-well site at one of the end spheres is studied. Isobaric-isothermal Monte Carlo simulations were performed for this model at subcritical and supercritical temperatures at a association strength typical of hydrogen-bonding systems. The theory is seen accurately to predict the simulation results subject to the limitations of the equation of state of the reference fluid. The system studied has some of the main complexities found in associating chain molecules such as organic acids, alkanols, and primary amines.
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    The ISM Equation of State Applied to Refrigerants (1999)
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    International journal of thermophysics 20 (1999), S. 1547-1555 
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    ISSN: 1572-9567
    Keywords: cohesive energy ; equation of state ; non-polar fluids ; refrigerants
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    Topics: Physics
    Notes: Abstract In this work, we apply an equation of state based on statistical–mechanical perturbation theory to liquid refrigerants and their mixtures. Three temperature-dependent parameters are needed to use the equation of state: the second virial coefficient, B 2(T), an effective van der Waals covolume, b(T), and a scaling factor, α(T). The second virial coefficients are calculated from a correlation based on the heat of vaporization, ΔH vap, and the liquid density at the freezing point, ρfp. α(T) and b(T) can also be calculated from the second virial coefficient by a scaling rule. Based on the theory, these two temperature-dependent parameters depend only on the repulsive branch of the potential function, and therefore, by our procedure, can be found from ΔH vap and ρfp. The theory has considerable predictive power, since it permits the construction of the p–v–T surface from the heat of vaporization plus the triple-point density. The equation of state is tested for pure, two- and three-component liquid refrigerant mixtures.
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    URL: http://dx.doi.org/10.1023/A:1021401407904
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    Equation of State for Molten Alkali Metal Alloys (1999)
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    International journal of thermophysics 20 (1999), S. 1575-1585 
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    Keywords: alkali metal alloys ; cohesive energy ; equation of state ; statistical mechanics ; surface tension
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    Notes: Abstract Calculated results of the liquid density of binary molten alloys of Na–K and K–Cs over the whole range of concentrations and that of a ternary molten eutectic of Na–K–Cs from the freezing point up to several hundred degrees above the boiling point are presented. The calculations were performed with the analytical equation of state proposed by Ihm, Song, and Mason, which is based on statistical-mechanical perturbation theory. The second virial coefficients were calculated from the corresponding-states correlation of Mehdipour and Boushehri. Calculation of the other two temperature-dependent parameters was carried out by scaling. The calculated results cover a much wider range of temperatures and are more accurate than those presented in our previous work.
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    Compressibilities of ternary mixtures C1-nC16-CO2 under pressure from ultrasonic measurements of sound speed (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 851-871 
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    ISSN: 1572-9567
    Keywords: compressibility ; equation of state ; high pressure ; speed of sound
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    Topics: Physics
    Notes: Abstract Speed of sound measurements have been performed on three mixtures of the ternary system methane + carbon dioxide + normal hexadecane. The systems have been investigated from 12 to 70 MPa in the temperature range from 313 to 393 K. Furthermore, these measurements have allowed the evaluation of the isothermal and the isentropic compressibilities up to 70 MPa from low pressure (〈40-MPa) density data.
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    Crossover equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 909-944 
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    ISSN: 1572-9567
    Keywords: critical phenomena ; equation of state ; ethane ; methane ; plait point ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present an equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region that incorporates the crossover from singular thermodynamic behavior near the locus of vapor-liquid critical points to regular thermodynamic behavior outside the critical region. The equation of state yields a satisfactory representation of the thermodynamic-property data for the mixtures in a large range of temperatures and densities.
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    Equation of state for compressed liquids from surface tension (1996)
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    International journal of thermophysics 17 (1996), S. 945-957 
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    ISSN: 1572-9567
    Keywords: compressed liquids ; corresponding states ; equation of state ; surface tension
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    Notes: Abstract A method for predicting an analytical equation of state for liquids from the surface tension and the liquid density at the freezing temperature (γ 1,ϱ 1) as scaling constants is presented. The reference temperature. Tref. is introduced and the product (T ref T 1 1 2 ) is shown to be an advantageous corresponding temperature for the second virial coeflicienls. B2(T). of spherical and molecular fluids. Thus, B2(T) follows a promising corresponding states principle and then calculations forα(T) andb(T), the two other temperature-dependent constants of the equation of state, are made possible by scaling. As a result, (γ 1,ϱ 1) are sufficient for the determination of thermophysical properties of fluids from the freezing line up to the critical temperature. The present procedure has the advantage that it can also be used in cases whereT c andP c are not known or the vapor pressure is too small to allow accurate measurements. We applied the procedure to predict the density of Lennard-Jones liquids over an extensive range of temperatures and pressures. The results for liquids with a wide range of acentric factor values are within 5%.
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    Thermodynamic Properties of Sulfur Hexafluoride (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 739-765 
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    ISSN: 1572-9567
    Keywords: Burnett measurements ; equation of state ; heat capacity ; intermolecular potential ; speed of sound ; sulfur hexafluoride ; SF6 ; thermodynamic properties ; vapor pressure ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present new vapor phase speed-of-sound data u(P, T), new Burnett density–pressure–temperature data ρ(P, T), and a few vapor pressure measurements for sulfur hexafluoride (SF6). The speed-of-sound data spanned the temperature range 230 K≤T≤460 K and reached maximum pressures that were the lesser of 1.5 MPa or 80% of the vapor pressure of SF6. The Burnett ρ(P, T) data were obtained on isochores spanning the density range 137 mol·m−3≤ρ≤4380 mol·m−3 and the temperature range 283 K≤T≤393 K. (The corresponding pressure range is 0.3 MPa≤P≤9.0 MPa.) The u(P, T) data below 1.5 MPa were correlated using a model hard-core, Lennard–Jones intermolecular potential for the second and third virial coefficients and a polynomial for the perfect gas heat capacity. The resulting equation of state has very high accuracy at low densities; it is useful for calibrating mass flow controllers and may be extrapolated to 1000 K. The new u(P, T) data and the new ρ(P, T) data were simultaneously correlated with a virial equation of state containing four terms with the temperature dependences of model square-well potentials. This correlation extends nearly to the critical density and may help resolve contradictions among data sets from the literature.
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    Chempak: Physical-Properties Database Structure and Development (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 771-779 
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    ISSN: 1572-9567
    Keywords: databases ; equation of state ; thermodynamic properties ; transport properties
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    Topics: Physics
    Notes: Abstract Chempak (commercial physical properties database and properties estimation software) gives the thermodynamic and transport properties of pure compounds as functions of temperature and pressure for both liquid and vapor phases. Compound liquid properties are defined from the melting to the critical points. Vapor properties are defined from the melting point to 1300 K. The user may define up to 50 mixtures of compounds drawn from the database. In addition, the user may add up to 100 additional compounds defined by using the same techniques employed to construct the main database. Vapor properties are defined by the use of the Lee–Kesler and the Wu and Stiel equations of state. Vapor viscosity and thermal conductivity are defined using corresponding states methods. Liquid thermodynamic properties (except specific heat) are derived from the equation of state. All other liquid properties are defined by setting 11 data values from the melting to the critical point. The resulting property data arrays are interpolated against temperature.
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    Thermodynamic Properties of Air from 60 to 2000 K at Pressures up to 2000 MPa (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 217-228 
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    ISSN: 1572-9567
    Keywords: air ; equation of state ; fundamental equation ; high pressure ; high temperature ; thermodynamic properties
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    Topics: Physics
    Notes: Abstract A thermodynamic property formulation for standard dry air based upon experimental P–ρ–T, heat capacity, and speed of sound data and predicted values, which extends the range of prior formulations to higher pressures and temperatures, is presented. This formulation is valid for temperatures from the solidification temperature at the bubble point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of experimental air data above 873 K and 70 MPa, air properties were predicted from nitrogen data. These values were included in the fit to extend the range of the fundamental equation. Experimental shock tube measurements ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 28 GPa. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the fundamental equation for the vapor is ±0.1%. The uncertainty in calculated liquid densities is ±0.2%. The estimated uncertainty of calculated heat capacities is ±1% and that for calculated speed of sound values is ±0.2%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is ±0.5%, increasing to ±1% at 2000 K and 2000 MPa.
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    Calculation of the compressibility factor of natural gases based on the calorific value and the specific gravity (1990)
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    International journal of thermophysics 11 (1990), S. 145-156 
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    ISSN: 1572-9567
    Keywords: calorific value ; compressibility factor ; equation of state ; natural gas ; mixtures ; specific gravity
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    Topics: Physics
    Notes: Abstract The measurement of large volume flows of natural gas in transmission lines requires an accurate equation of state for pressures up to about 12 MPa and in the temperature range from 265 to 335 K. If a detailed analysis of the gas mixture is available, one of the possibilities is to use the virial equation of state. However, such a gas analysis is time-consuming and expensive and, therefore, not always practical. We have developed a new equation which is based on the virial equation but requires limited input data. In general, for any given natural gas, the gross calorific value, the specific gravity, and the mole fractions of nitrogen and carbon dioxide are known. It will be shown that a knowledge of three of these four quantities is sufficient for an accurate prediction of the compressibility factor of the natural gas.
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    An interim analytic equation of state for sulfurhexafluoride (1990)
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    International journal of thermophysics 11 (1990), S. 189-199 
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    ISSN: 1572-9567
    Keywords: equation of state ; saturation properties ; Sulfurhexafluoride ; thermodynamic properties
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    Topics: Physics
    Notes: Abstract An interim analytic equation of state for Sulfurhexafluoride is given in the form of a reduced Helmholtz energy function. It represents the thermodynamic properties over the temperature range 222.38 to 525 K for pressures up to 55 MPa. The data selected for determining the linear coefficients of the equation are given, which includes some values predicted using the principle of corresponding states. The method used for the multiproperty fitting is given and, in particular, the functions used for fitting isobaric heat capacities as primary data. Comparisons with values predicted by the equation of state are given for saturation properties, second virial coefficients, densities, and isobaric and isochoric heat capacities. The accuracy of the representation of the equation of state is discussed and, also, the problems arising from inconsistencies between the different data sets. The interim status of this equation of state is due to these inconsistencies.
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    Compressibility of liquids: Theoretical basis for a century of empiricism (1991)
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    International journal of thermophysics 12 (1991), S. 855-868 
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    Keywords: argon ; equation of state ; Lennard-Jones fluid ; liquid compressibility ; Tait equation
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    Topics: Physics
    Notes: Abstract We show how the successful empirical results of the past century for the compressibility of liquids can be obtained from a recent statistical-mechanical theory that includes dense fluids as well as low-density gases and vapors. The theory also shows to what extent the results for liquids can be extended to dense supercritical fluids and how they can be generalized to any number of dimensions. For simplicity only argon and a Lennard-Jones (12,6) fluid are examined in detail, but the results can probably be extended to real molecular fluids.
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    Equation of state for mixtures of nonpolar fluids: Prediction from experimental constants of the components (1992)
    Springer
    International journal of thermophysics 13 (1992), S. 1053-1060 
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    Keywords: equation of state ; gases ; mixtures ; nonpolar fluids
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    Topics: Physics
    Notes: Abstract We present a simple procedure by which an analytical equations of state for a mixture of normal fluids can be predicted from the constantsT c (critical temperature),p c (critial pressure), and ω (Pitzer acentric factor) for each pure component. The equation covers the range from the dilute vapor or gas to the highly compressed liquid or supercritical fluid.
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    P-V-T-x measurements of aqueous mixtures at supercritical conditions (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 231-250 
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    Keywords: aqueous mixtures ; compressibility factor ; equation of state ; excess Gibbs free energy ; excess volume ; hydrocarbons ; supercritical fluids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We report P-V-T-x measurements for five binary systems: water+methane, water+n-hexane, water+n-octane, water+benzene, and water+nitrogen at supercritical conditions for several compositions. The experimental data were obtained along isotherms with a phase-equilibrium cell designed for accurate measurements at pressures up to 100 MPa. The uncertainties in temperature, pressure, density, and concentration are ±0.01 K, ±0.2%, ±0.2%, and ±0.002 mole fractions, respectively. The behavior of the second virial coefficient, the excess volume, and the excess Gibbs free energy is also discussed.
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    Transport properties of 1,1,1,2-tetrafluoroethane (R134a) (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 951-988 
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    ISSN: 1572-9567
    Keywords: 1,1,1,2-tetrafluoroethane ; correlation ; critical region ; equation of state ; HFC-134a ; R134a ; thermal conductivity ; transport properties ; viscosity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract New equations for the thermal conductivity and the viscosity of R134a that are valid in a wide range of pressures and temperatures are presented. They were obtained through a theoretically based, critical evaluation of the available experimental data, which showed considerable inconsistencies between data sets, in particular in the vapor phase. In the critical region the observed enhancement in the thermal conductivity is well represented by a crossover model for the transport properties of fluids. Since thermodynamic properties enter into the calculation of the critical enhancement of the transport properties, a new fundamental equation for the critical region was developed also.
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    Thermodynamic behavior of mixtures of methane and ethane in the critical region (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 1187-1200 
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    Keywords: binary mixtures ; critical phenomena ; equation of state ; ethane ; methane ; plait point ; specific heat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An isomorphic equation of state for near-critical binary mixtures is used to represent equation of state and specific heat data for mixtures of methane and ethane in a substantial range of densities and temperatures around the critical line.
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    Thermodynamic behavior of mixtures of methane and ethane in the critical region (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 1187-1200 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; critical phenomena ; equation of state ; ethane ; methane ; plait point ; specific heat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An isomorphic equation of state for near-critical binary mixtures is used to represent equation of state and specific heat data for mixtures of methane and ethane in a substantial range of densities and temperatures around the critical line.
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    Measurements of the p-v-T behavior of refrigerant R134a in the liquid phase (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 727-738 
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    ISSN: 1572-9567
    Keywords: equation of state ; p-v-T measurements ; R134a ; refrigerants ; 1, 1, 1, 2-tetrafluoroethane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A short description of an improved p-v-T apparatus with a constant-volume piezometer is given. p-v-T data of the environmentally safe refrigerant 1, 1, 1, 2-tetrafluoroethane (R134a), were measured for temperatures between 205 and 309 K at pressures up to 56 MPa. The uncertainty of temperature and pressure measurements was estimated to be ±0.05°C and ±0.1%, respectively; uncertainty in the specific volume was estimated to be ±0.15%. Purity of the sample used was 99.9+wt%. The data are represented analytically in order to demonstrate experimental accuracy and to facilitate calculation of thermodynamic properties.
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    A new nonrandom lattice fluid model and its simplification by two-liquid theory for phase equilibria of complex mixtures (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 723-731 
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    ISSN: 1572-9567
    Keywords: complex mixtures ; equation of state ; multiphase equilibria ; nonrandom lattice theory ; polymer solutions ; supercritical fluids
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    Notes: Abstract A new riogorous equation of state (EOS) and its simplified version have been proposed by the present authors based on the full Guggenheim combinatorics ] of the nonrandom lattice hole theory. The simplified EOS. with the introduction of the concept of local composition, becomes similar to the density-dependent UNIQUAC model. However, im the present approach we have a volumetric EOS instead of the excess Gibbs function. Both EOSs were tested for their applicability in correlating the phase equilibria behavior of pure components and complex mixtures. Comparison of both models with experiment includes such systems as nonpolar nonpolar, nonpolar polar, and polar polar hydrocarbons, supercritical systems, and polymer solutions. With two parameters for each pure component and one binary interaction energy parameter, results obtained to date demonstrate that both formulations are quantitatively applicable to complex systems oer a wide range of temperatures, pressures, and concentrations.
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    Thermodynamic properties of the generalized Murnaghan equation of state of solids (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1009-1026 
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    ISSN: 1572-9567
    Keywords: Anderson-Grüneisen ; bulk modulus ; equation of state ; expansivity ; high pressure ; Murnaghan equation
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    Topics: Physics
    Notes: Abstract In the Murnaghan approximation, an isothermal relation between pressure (P) and volume (V) for solids is derived from the assumption that the isothermal bulk modulus (B) is a linear function ofP. This paper presents a thermodynamic analysis of a generalized form of the equation, based on treating all its various parameters [viz., V, B, and (∂B/∂P) T atP=0] as functions of temperature. Extending a previous study, the effect ofT upon (∂B/∂P) T is accounted for by using a dimensionless parameter introduced by us, which is used in formulating general expressions for the volume dependence of various thermophysical quantities,viz., the thermal expansion coefficient (α), the productαB, and the Grüneisen and Anderson-Grüneisen parameters. Some combinations of these parameters are identified, which show a simple dependence uponP. The new expressions are used in analyzing current approximations and the behavior of the solid in the low-compression range. In particular, an expression forα at highP is reported which generalizes the Anderson equation and previous results by us.
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    Application of nonlinear regression in the development of a wide range formulation for HCFC-22 (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1155-1164 
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    ISSN: 1572-9567
    Keywords: chlorodifluoromethane ; equation of state ; HCFC-22 ; nonlinear fitting ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An equation of state has been developed for HCFC-22 for temperatures from the triple point (115.73 K) to 550 K, at pressures up to 60 MPa. Based on comparisons between experimental data and calculated properties, the accuracy of the wide-range equation of state is ±0.1% in density, ±0.3% in speed of sound, and ±1.0% in isobaric heat capacity, except in the critical region. Nonlinear fitting techniques were used to fit a liquid equation of state based onP-ρ-T, speed of sound, and isobaric heat capacity data. Properties calculated from the liquid equation of state were then used to expand the range of validity of the wide range equation of state for HCFC-22.
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    Vapor-liquid equilibrium, coexistence curve, and critical locus for binary HFC-32/HFC-134a mixture (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1175-1184 
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    ISSN: 1572-9567
    Keywords: binary interaction parameter ; critical density ; critical temperature ; equation of state ; R-32/134a mixture ; vapor-liquid coexistence curve ; vapor-liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Two kinds of equilibrium measurements of binary R-32/134a mixtures were carried out. The vapor-liquid equilibria were measured by the static method in the temperature range between 283 and 313 K. On the basis of the present experimental data, the temperature dependence of the binary interaction parameterk 12 for two equations of state, namely, the Soave-Redlich-Kwong equation and Carnahan-Starling-De Santis equation, was discussed. The vapor-liquid coexistence curve near the critical point was also measured by the observation of meniscus disappearance. The critical temperatures and critical densities of 30 and 70 wt% R-32 mixtures were determined on the basis of the saturation densities along the coexistence curve in the critical region. In addition, a correlation of the critical locus for this mixture is proposed as a function of composition.
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    The use of an MHV-2 equation of state for modeling the thermodynamic properties of refrigerant mixtures (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1165-1174 
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    ISSN: 1572-9567
    Keywords: activity coefficient ; equation of state ; MHV-2 ; refrigerants ; R32 ; R134a ; R125 ; vapor-liquid equilibria
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    Notes: Abstract This paper reports on the development and application of a thermodynamic model based on the second-order Modified Huron Vidal equation of state (MHV-2) to predict the properties of ternary mixtures of the refrigerants R32, R125, and R134a. The mixing rules of this equation of state have been used to incorporate directly an activity-coefficient model for the excess Gibbs free energy. The parameters for the activity-coefficient model have been derived from experimental VLE data for binary mixtures. This methodology has enabled the production of a thermodynamically consistent model which can be used to predict the phase equilibria of R32/R125/R134a mixtures. The input data used in the model are presented in the paper and the predictions of the model are compared with available experimental data. The model has been used to predict the behavior of ternary refrigerant blends of R32/R125/R134a in fractionation scenarios, such as liquid charging and vapor leakage, which are of direct interest to the refrigeration industry. Details of these applications and comparisons with experimental data are discussed, along with other general uses of the thermodynamic model.
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    Prediction of multiphase equilibria in associating fluids by a contact-site quasichemical equation of state (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1287-1297 
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    Keywords: associating fluids ; contact-site model ; equation of state ; group contribution ; monomer fraction ; multiphase equilibria
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    Notes: Abstract A contact-site quasichemical equation of state has been used Tor the modeling of different kinds of fluid phase equilibria (between a gas phase and one or more liquids) over a wide range of conditions. Among the systems of interest are the ternary mixtures water + alkanols + hydrocarbons (alkanes or alkynes), water + alkanols (or acetone)+ CO2, water + polyoxyethyleneglycol ethers + heavy alkanes. The model has been applied to describing the thermodynamic properties of the binary subsystems and to predict the phase behavior of the ternary systems. For longer-chain alkanols and hydrocarbons a group-contribution approach is implemented, which allows the modeling when no experimental data are available. The model gives reasonable predictions of phase behavior and the correct trends in the calculated phase diagrams in most cases. The concentrations of associates in liquid and gas phases are estimated by the model and compared with some experimental and computer simulation data. The predictive abilities of the model, its limitations, and possible ways of its improvement are discussed.
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    A New equation of state for square-well molecules (1995)
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    International journal of thermophysics 16 (1995), S. 1277-1286 
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    ISSN: 1572-9567
    Keywords: equation of state ; molecular simulation ; perturbation theory ; second virial coefficient ; square-well molecules
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    Notes: Abstract This paper presents a new equation of state for the square-well fluid based on perturbation theory. This equation has the exact second virial coefficient behavior, converges to the correct mean-field behavior at high densities, and accurately interpolates between the two limits. Monte Carlo simulations were performed to evaluate the limiting behavior of the theory in the dilute-gas regime. Comparison of the theory with the simulation results shows excellent agreement between the equation-of-state predictions and the data.
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    Ideal-gas thermodynamic properties for natural-gas applications (1995)
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    International journal of thermophysics 16 (1995), S. 1381-1392 
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    Keywords: caloric properties ; equation of state ; ideal gas ; isobaric heat capacity ; natural gas ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Calculating caloric properties from a thermal equation of state requires information such as isobaric heat capacities in the ideal-gas state as a function of temperature. In this work, values for the parameters of thec p 0 correlation proposed by Aly and Lee were newly determined for 21 pure gases which are compounds of natural gas mixtures. The values of the parameters were adjusted to selectedc p 0 data calculated from spectroscopic data for temperatures ranging from 10 to 1000 K. The data sources used are discussed and compared with literature data deduced from theoretic models and caloric measurements. The parameters presented will be applied in a current GERG project for evaluating equations of state (e.g., the AGA 8 equation) for their suitability for calculating caloric properties.
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    An analytical method of predicting Lee-Kesler-Plöcker equation-of-state binary interaction coefficients (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1393-1411 
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    ISSN: 1572-9567
    Keywords: computer algorithm ; binary interaction coefficient ; equation of state ; mixture ; nonpolar and polar substances ; thermodynamic properties ; reduced properties
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    Notes: Abstract An analytical method is proposed for finding numerical values of binary interaction coefficients for the Lee-Kesler-Plöcker (LKP) equation of state. The method is based on solving simultaneous equations from Plöcker's mixing rules for pseudocritical parameters of a mixture and the Lee-Kesler equation for the saturation line. For mixtures of hydrocarbons containing from two to nine carbon atoms, the divergence between calculated and experimentally based interaction coefficients (ICs) is no more than ±0.4%. The method is extended to mixtures of polar substances. For polar mixtures, aneffective molar composition concept is introduced which takes into account the impact of dipole moments on the process of molecular associations. Formulas for finding the effective molar composition of mixtures containing polar and/or nonpolar constituents and the binary interaction coefficient (κ ij) based on this effective composition and pure component properties are shown. Calculatedκ ij values for 12 binary mixtures of polar substances differ by 0.4 % or less from correspondingκ ij values obtained by processing experimental data on saturated pressure (P s) and saturated temperature (T s) lines for these same mixtures. A simplified alternativeκ ij approximation method with an error (2–5 %) is also given for mixtures of polar substances.
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    A corresponding-states principle for the equation of state of linear homonuclear fused-hard-sphere fluids (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 1413-1419 
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    ISSN: 1572-9567
    Keywords: equation of state ; corresponding states ; fused-hard-sphere fluids ; hard spheres
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    Notes: Abstract A theoretically based corresponding-states principle previously developed for the equation of state of hard-convex-body fluids is extended to rigid linear homonuclear fused-hard-sphere fluids. Effective volumes and shapes are introduced in order to account for the nonconvexity of the molecules. The excess compressibility factor, reduced by means of a parameter which can be determined analytically, is a common function of the effective packing fraction. The analytical expression for the function can be obtained from the equation of state of the hard-sphere fluid. Existing simulation data for diatomics, triatomics and tetraatomics show excellent agreement with the corresponding-states principle.
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    An analytical equation of state for molten alkali metals (1995)
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    International journal of thermophysics 16 (1995), S. 1429-1438 
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    Keywords: cohesive energy ; equation of state ; molten alkali metals ; statistical mechanics
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    Topics: Physics
    Notes: Abstract This paper brings the molten alkali metals into the scope of a new statistical mechanical equation of state that is known to satisfy normal fluids over the whole range. As for normal fluids, the latent heat of vaporization and density at freezing temperature are the only inputs (scaling factors). The correspondingstates correlation of normal fluids is used to calculate the second virial coefficient,B 2(T), of alkali metals, which is scarce experimentally and its calculation is complicated by dimer formation. Calculations of the other two temperature-dependent constants,α(T) andb(T), follow by scaling. The virial coefficients of alkali metals cannot be expected to obey a law of corresponding states for normal fluids. The fact that two potentials are involved may be the reason for this. Thus, alkali metals have the characteristics of interacting through singlet and triple potentials so that the treatment by a single potential here is fortuitous. The adjustable parameter of the equation of state,γ, compensates for the uncertainties inB 2(T). The procedure used to calculate the density of liquids Li through Cs from the freezing line up to several hundred degrees above the boiling temperatures. The results are within 5 %.
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    Solubilities of long-chain hydrocarbons in carbon dioxide (1996)
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    International journal of thermophysics 17 (1996), S. 23-33 
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    Keywords: equation of state ; heavy hydrocarbons ; natural gas ; supercritical carbon dioxide ; wax deposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Heavy hydrocarbons are becoming an increasingly important problem for the natural gas industry as it develops more costly gas reserves, such as those in the deep Gulf of Mexico. The waxy substances precipiate during natural gas processing, causing blockage of transmission pipelines. Knowledge of the solubility behavior of these hydrocarbon solids is therefore necessary to develop solutions to the solid deposition problem. This work reports solid-supercritical fluid equilibrum data for long-chain n-alkanes in carbon dioxide, a component of natural gas, over a range of temperatures and pressures that are typical of natural gas processing. A flow apparatus was used to measure the solubility, and the data were correlated by the Patel-Teja equation of state. Satisfactory agreement was obtained between calculated and experimental values, so the equation of state may be used to estimate the conditions for solid deposition and the amounts of solids formed at typical processing conditions.
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    An accurate Van der Waals-type equation of state for the Lennard-Jones fluid (1996)
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    International journal of thermophysics 17 (1996), S. 391-404 
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    Keywords: coexistence curve ; equation of state ; Lennard Jones fluid ; thermodynamic properties
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    Notes: Abstract A new equation of state (EOS) is proposed for the Helmholtz energyF of the Lennard Jones fluid which represents the thermodynamic properties over a wide range of temperatures and densities. The EOS is written in the form of a generalized van der Waals equation.F =F u +F v. WhereF u is a hard body contribution andF A an anttractive dispersion force contribution. The expression forF H is closely related to the hybrid Barker Henderson pertubation theory. The construction ofF A is accomplished with the Setzmann Wagner optimization procedure on the basis of virial coefficients and critically assessed computer simulation data. A comparison with the EOS of Johnson et al. shows improvement in the description of the vapor liquid coexistence properties, thepvT data. and in peculiar, of the calorie properties. A comparison with the EOS of Kolafa and Nezbeda which appeared after the bulk of this work was finished shows still by about 30%.
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    Thermophysical Properties of Gaseous CF4 and C2F6 from Speed-of-Sound Measurements (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 455-484 
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    ISSN: 1572-9567
    Keywords: CF4 ; C2F6 ; equation of state ; hexafluoroethane ; speed of sound ; tetrafluoromethane ; thermodynamic properties ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A cylindrical resonator was employed to measure the sound speeds in gaseous CF4 and C2F6. The CF4 measurements span the temperature range 300 to 475 K, while the C2F6 measurements range from 210 to 475 K. For both gases, the pressure range was 0.1 MPa to the lesser of 1.5 MPa or 80% of the sample’s vapor pressure. Typically, the speeds of sound have a relative uncertainty of less than 0.01 % and the ideal-gas heat capacities derived from them have a relative uncertainty of less than 0.1%. The heat capacities agree with those determined from spectroscopic data. The sound speeds were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two models for the virial coefficients were employed, one based on square-well potentials and the second based on a Kihara spherical-core potential. The resulting virial equations reproduce the sound-speed measurements to within 0.005 % and yield densities with relative uncertainties of 0.1% or less. The viscosity calculated from the Kihara potential is 2 to 11% less than the measured viscosity.
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    Thermodynamic Properties of Mixtures of R-32, R-125, R-134a, and R-152a (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1629-1638 
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    Keywords: equation of state ; mixtures ; R-32 ; R-125 ; R-134a ; R-152a ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A mixture model explicit in Helmholtz energy has been developed that is capable of predicting thermodynamic properties of refrigerant mixtures containing R-32, R-125, R-134a, and R-152a. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single equation that is applied to all mixtures used in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate thermodynamic properties of mixtures, including dew and bubble point properties and critical points, generally within the experimental uncertainties of the available measured properties. It incorporates the most accurate published equation of state for each pure fluid. The estimated uncertainties of calculated properties are ±0.25% in density, ±0.5% in the speed of sound, and ±1% in heat capacities. Calculated bubble point pressures are generally accurate to within ±1%.
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    An Equation of State for 1,1,1-Trifluoroethane (R-143a) (1999)
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    International journal of thermophysics 20 (1999), S. 1639-1651 
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    ISSN: 1572-9567
    Keywords: alternative refrigerant ; equation of state ; Helmholtz energy ; R-143a ; 1,1,1-trifluoroethane
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract A fundamental equation of state has been developed for 1,1,1-trifluoroethane (R-143a) using the dimensionless Helmholtz energy. The experimental thermodynamic property data, which cover temperatures from the triple point (161 K) to 433 K and pressures up to 35 MPa, are used to develop the present equation. These data are represented by the present equation within their reported experimental uncertainties: ±0.1% in density for both vapor and liquid phase P–ρ–T data, ±1% in isochoric specific heat capacities, and ±0.02% in the vapor phase speed-of-sound data. The extended range of validity of the present model covers temperatures from 160 to 650 K and pressures up to 50 MPa as verified by the thermodynamic behavior of the isobaric heat-capacity values over the entire fluid phase.
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    Determination of Second Virial Coefficients and Virial Equations of R-32 (Difluoromethane) and R-125 (Pentafluoroethane) Based on Speed-of-Sound Measurements (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1677-1688 
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    ISSN: 1572-9567
    Keywords: alternative refrigerant ; equation of state ; hydrofluorocarbon ; R-32 ; R-125 ; second virial coefficient ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The second virial coefficients, B, for difluoromethane (R-32, CH2F2) and pentafluoroethane (R-125, CF3CHF2) are derived from speed-of-sound data measured at temperatures from 273 to 343 K with an experimental uncertainty of ±0.0072%. Equations for the second virial coefficients were established, which are valid in the extensive temperature ranges from 200 to 400 K and from 240 to 440 K for R-32 and R-125, respectively. The equations were compared with theoretically derived second virial coefficient values by Yokozeki. A truncated virial equation of state was developed using the determined equation for the virial coefficients. The virial equation of state represents our speed-of-sound data and most of the vapor PρT data measured by deVries and Tillner-Roth within ±0.01 and ±0.1%, respectively.
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    Application of New, Modified BWR Equations of State to the Corresponding-States Prediction of Natural Gas Properties (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1721-1735 
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    Keywords: corresponding states ; density ; equation of state ; Lee–Kesler ; natural gas mixtures ; n-heptane ; n-pentane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The accurate description of mixtures includes both single-phase (bulk) properties and the location of phase equilibrium boundaries, e.g., properties that depend upon partial molar properties. In order to estimate these properties, many variants of corresponding-states theory have been developed, especially for nonpolar mixtures such as those found in natural gas systems, In this work we have developed two new, modified BWR equations of state for two natural gas components (n-pentane and n-heptane) and used these equations in a reformulated (Teja-like) Lee–Kesler model. The reformulated model has been tested on bulk-phase properties of hydrocarbon systems, in both the pure and the mixed states. Results have been obtained using the original Lee–Kesler model, the extended corresponding-states theory, and the multifluid corresponding-states principle using several combinations of reference fluids chosen from this and previous equation of state studies. Details of the new equations of state and theoretical comparisons are reported.
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    Prediction of Critical Properties of Mixtures from the PRSV-2 Equation of State: A Correction for Predicted Critical Volumes (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1557-1574 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; critical properties ; critical volume ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state (1986) for critical properties of binary mixtures was investigated. The procedure adopted by Heidemann and Khalil (1980) and discussed by Abu-Eishah et al. (1998) was followed. An optimized value for the binary interaction parameter based on minimization of error between experimental and predicted critical temperatures was used. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for several nonpolar and polar systems agree well with experimental data and are always better than those predicted by the group-contribution method. A correction is introduced here to modify the predicted critical volume by the PRSV-2 equation of state, which makes the average deviations between predicted and experimental values very close to or even better than those predicted by the group-contribution method.
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    Speed of Sound in the Liquid Phase of the R134a/152a Refrigerant Blend (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1689-1697 
    Details
    ISSN: 1572-9567
    Keywords: equation of state ; experimental method ; phase equilibrium parameters ; refrigerant ; speed of sound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The speed of sound in the liquid phase of the binary blend of R134a and R152a and its components has been studied. The speed of sound was measured by means of the impulse method at a frequency of 2.1 MHz. The temperature range was 230 to 350 K at pressures up to 16 MPa. The values of speed of sound were measured with a standard error of not more than 0.25%. The results obtained for both components of the blend are represented with expressions based on a physical model. The standard deviation (versus the model) of the measured data is 0.09%, On the basis of the results obtained, the Redlich–Kister correlation has been used over the entire ranges of composition, temperature, and pressure to determine the speed of sound in the liquid phase and at the bubble point of the blend investigated.
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    URL: http://dx.doi.org/10.1023/A:1022653828617
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    Thermophysical Properties of Gaseous HBr and BCl3 from Speed-of-Sound Measurements (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 805-829 
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    ISSN: 1572-9567
    Keywords: BCl3 ; boron trichloride ; equation of state ; HBr ; hydrogen bromide ; speed of sound ; thermodynamic properties ; transport properties ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The speed of sound in gaseous hydrogen bromide (HBr) and boron trichloride (BCl3) was measured using a highly precise acoustic resonance technique. The HBr speed-of-sound measurements span the temperature range 230 to 440 K and the pressure range from 0.05 to 1.5 MPa. The BCl3 speed-of-sound measurements span the temperature range 290 to 460 K and the pressure range from 0.05 MPa to 0.40 MPa. The pressure range in each fluid was limited to 80% of the sample vapor pressure at each temperature. The speed-of-sound data have a relative standard uncertainty of 0.01%. The data were analyzed to obtain the ideal-gas heat capacities as a function of temperature with a relative standard uncertainty of 0.1%. The heat capacities agree with those calculated from spectroscopic data within their combined uncertainties. The speeds of sound were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two virial coefficient models were employed, one based on the hard-core square-well intermolecular potential model and the second based on the hard-core Lennard–Jones intermolecular potential model. The resulting virial equations of state reproduced the speed-of-sound measurements to 0.01% and can be expected to calculate vapor densities with a relative standard uncertainty of 0.1%. Transport properties calculated from the hard-core Lennard–Jones potential model should have a relative standard uncertainty of 10% or less.
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    URL: http://dx.doi.org/10.1023/A:1006627306105
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    Thermodynamic Properties of Sutherland Fluids from an Analytical Perturbation Theory (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 899-908 
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    ISSN: 1572-9567
    Keywords: Barker–Henderson perturbation theory ; equation of state ; hard-sphere fluid ; radial distribution function ; Sutherland potential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Analytical expressions are obtained for the thermodynamic properties of fluids with potentials consisting of a spherical hard core plus an attractive tail of the form 1/r γ (Sutherland fluids). To this end, use is made of the Barker–Henderson perturbation theory together with an analytical expression for the first coordination shell of the radial distribution function of the reference hard-sphere fluid. This expression was derived previously on the basis of the analytical solution of the Percus–Yevick integral equation theory. The results are compared with available simulation data for a wide range of densities, temperatures, and values of the potential parameter γ. The overall agreement is good, and the accuracy is similar to that obtained using more accurate solutions for the radial distribution function of the hard-sphere fluid leading to nonanalytical expressions for the thermodynamic properties of the fluid considered.
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    URL: http://dx.doi.org/10.1023/A:1006614324761
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    Vapor–Liquid Equilibria for the 1,1,1-Trifluoroethane (HFC-143a)+1,1,1,2-Tetrafluoroethane (HFC-134a) System (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 871-881 
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    ISSN: 1572-9567
    Keywords: binary interaction parameters ; equation of state ; HFC-134a ; HFC-143a ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A vapor–liquid equilibrium apparatus has been developed and used to obtain data for the binary HFC-143a+HFC-134a system. Fifty-four equilibrium data are obtained for the HFC-143a+HFC-134a system over the temperature range from 263.15 to 313.15 K at 10 K intervals. The experimental data were correlated with the Carnahan–Starling–De Santis (CSD) and Peng–Robinson (PR) equations of state. Based upon the present data, the binary interaction parameters for the CSD and PR equations of state were calculated for six isotherms for the HFC-143a+HFC-134a system. The binary interaction parameters for both equations of state were fitted by a linear equation as a function of temperature. The present data were in good agreement with the calculated results from the CSD equation of state, and the deviations were less than 1.0% with the exception of two points.
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    Crossover SAFT Equation of State and Thermodynamic Properties of Propan-1-ol (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1373-1405 
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    ISSN: 1572-9567
    Keywords: associating fluids, critical state ; crossover theory ; equation of state ; enthalpies ; heat capacities ; n-alkanols ; thermodynamic properties ; speed of sound ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this work we have developed a new equation of state (EOS) for propan-1-ol on the basis of the crossover modification (CR) of the statistical-associating-fluid-theory (SAFT) EOS recently developed and applied to n-alkanes. The CR SAFT EOS reproduces the nonanalytical scaling laws in the asymptotic critical region and reduces to the analytical-classical SAFT EOS far away from the critical point. Unlike the previous crossover EOS, the new CR SAFT EOS is based on the parametric sine model for the universal crossover function and is able to represent analytically connected van der Waals loops in the metastable fluid region. The CR SAFT EOS contains 10 system-dependent parameters and allows an accurate representation of the thermodynamic properties of propan-1-ol over a wide range thermodynamic states including the asymptotic singular behavior in the nearest vicinity of the critical point. The EOS was tested against experimental isochoric and isobaric specific heats, speed of sound, PVT, and VLE data in and beyond the critical region. In the one-phase region, the CR SAFT equation represents the experimental values of pressure with an average absolute deviation (AAD) of less than 1% in the critical and supercritical regions and the liquid densities with an AAD of about 1%. A corresponding states principle is used for the extension of the new CR SAFT EOS for propan-1-ol to higher n-alkanols.
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    URL: http://dx.doi.org/10.1023/A:1006657410862
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    Molar Heat Capacity Cv, Vapor Pressure, and (p, ρ, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for Chlorotrifluoromethane (R13) (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1097-1121 
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    ISSN: 1572-9567
    Keywords: calorimeter ; chlorotrifluoromethane ; density ; equation of state ; heat capacity ; isochoric ; liquid ; R13 ; vapor ; vapor pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Measurements of the molar heat capacity at constant volume C v for chlorotrifluoromethane (R13) were conducted using an adiabatic method. Temperatures ranged from 95 to 338 K, and pressures were as high as 35 MPa. Measurements of vapor pressure were made using a static technique from 250 to 302 K. Measurements of (p, ρ, T) properties were conducted using an isochoric method; comprehensive measurements were conducted at 15 densities which varied from dilute vapor to highly compressed liquid, at temperatures from 92 to 350 K. The R13 samples were obtained from the same sample bottle whose mole fraction purity was measured at 0.9995. A test equation of state including ancillary equations was derived using the new vapor pressures and (p, ρ, T) data in addition to similar published data. The equation of state is a modified Benedict–Webb–Rubin type with 32 adjustable coefficients. Acceptable agreement of C v predictions with measurements was found. Published C v(ρ, T) data suitable for direct comparison with this study do not exist. The uncertainty of the C v values is estimated to be less than 2.0% for vapor and 0.5% for liquid. The uncertainty of the vapor pressures is 1 kPa, and that of the density measurements is 0.1%.
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    URL: http://dx.doi.org/10.1023/A:1026446004383
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    Aqueous Electrolytes at Near-Critical and Supercritical Temperatures (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 355-366 
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    ISSN: 1572-9567
    Keywords: aqueous electrolytes ; calcium chloride ; equation of state ; near-critical properties ; phase-diagram type ; potassium chloride ; sodium chloride ; supercritical properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The aqueous electrolyte systems $${\text{NaCl - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O, KCl}}{\kern 1pt} {\text{ - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O and CaCl}}{\kern 1pt} {\text{ - H}}_{\text{2}} {\text{O}}$$ are of great interest both geologically and industrially. Equations of state were developed recently for these systems; they are based on theoretical modeling for mixtures of hard spheres with appropriate diameters and dipole moments for H2O, NaCl, and KCl and with a quadrupole moment for CaCl2. Empirical terms are added as required to fit the available experimental data. The fit to the compositions and densities at equilibrium of the saturated vapor and liquid constitutes a severe test, in addition to properties in the single-phase regions. Temperatures range upward from 300°C for NaCl and KCl and from 250°C for CaCl2 for these equations. Complications from hydrolysis and alternate equations valid at lower temperatures are discussed briefly. In addition, there is a very important theoretical aspect relating to the general phase diagrams. With the high ratio of critical temperatures of the salts to that of water, complex diagrams involving liquid–liquid phase separation near the critical point of water are expected. But no such effect is observed experimentally; instead, one finds simple type I phase diagrams. This is particularly clear in the case of $${\text{NaCl - }}{\kern 1pt} {\text{H}}_{\text{2}} {\text{O}}$$ , where the database is very accurate and extends above 1000 K.
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    Mixing Rules for van der Waals-Type Equations of State Based on Activity-Coefficient Models (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 1429-1445 
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    ISSN: 1572-9567
    Keywords: activity coefficient models ; equation of state ; excess functions ; mixing rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new approach for incorporation of the excess free energy from an activity coefficient model (ACM) into an equation of state (EOS) has been proposed. The approach is based on a concept that any ACM is valid at a low but finite value of compressibility factor. This condition allows us to analyze the “infinite pressure” approximation in a general way. It is shown that the “infinite pressure” approach neglects the contribution of the repulsive term of the EOS to the excess free energy of a mixture. This, in turn, introduces inconsistency which results in the difference in the calculated excess free energy of the EOS and the base ACM. The new approach defines parameter a of the EOS as an implicit function of compositions and temperature, thus requiring an iterative procedure using the “infinite pressure limit” as a starting point. The new approach can be modified to provide the correct composition dependence of a mixture second virial coefficient. Applicability of the new method has been tested for binary systems under vapor–liquid and liquid–liquid equilibrium conditions.
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    Thermodynamic Properties for R-404A (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 129-140 
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    ISSN: 1572-9567
    Keywords: correlation ; equation of state ; R-125 ; R-134a ; R-143a ; R-404A ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An 18-coefficient modified Benedict–Webb–Rubin equation of state has been developed for R-404A, a ternary mixture of 44% by mass of pentafluoroethane (R-125), 52% by mass of 1,1,1-trifluoroethane (R-143a), and 4% by mass of 1,1,1,2-tetrafluoroethane (R-134a). Correlations of bubble point pressures, dew point pressures, saturated liquid densities, and saturated vapor densities are also presented. This equation of state has been developed based on the reported experimental data of PVT properties, saturation properties, and isochoric heat capacities by using least-squares fitting. These correlations are valid in the temperature range from 250 K to the critical temperature. This equation of state is valid at pressures up to 19 MPa, densities to 1300 kg·m−3, and temperatures from 250 to 400 K. The thermodynamic properties except for the saturation pressures are calculated from this equation of state.
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    A field-space conformai solution method (1990)
    Springer
    International journal of thermophysics 11 (1990), S. 49-59 
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    ISSN: 1572-9567
    Keywords: binary mixture ; conformal solution ; corresponding states ; critical phenomena ; equation of state ; field space ; mixtures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We propose a radical extension of the principle of corresponding states to mixtures. All previous methods of which we are aware are based upon the application of “mixing rules” which are explicit in the compositions of the resultant, or target, mixture. In the present development these relations are functions of field variables alone, specifically the activities of the reference system. This has a profound effect upon the basic machinery of the transformations. For example, when the new method is used to map the properties of a binary fluid mixture onto those of a pure fluid (and in contrast to the description of a mixture by one-fluid theory with van der Waals mixing rules), the dew-bubble-point surface of the mixture is mapped onto the vapor pressure curve of the pure fluid, and the critical line of the mixture is mapped onto the critical point of the pure fluid. Thus, there is no separate “pseudocritical” locus. The principal technical advantage of such a development is numerical; calculation of the location of vapor-liquid coexistence and critical manifolds is enormously simplified. The most important theoretical aspect associated with the new method is that if the reference system is described by an equation of state which obeys the critical scaling laws, then the entire critical manifold of the target system will also exhibit critical scaling.
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    Mixture equations of state: Composition dependence (1990)
    Springer
    International journal of thermophysics 11 (1990), S. 373-380 
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    ISSN: 1572-9567
    Keywords: composition dependence ; equation of state ; hybrid mixing rules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper discusses theoretical models for the composition dependence of equations of state and compares the quality of predictions against experimental thermodynamic property data. The mean density approximation (MDA) and the van der Waals one-fluid (VDW1) model are compared with hybrid mixing rules (HMR), in which rigorous composition dependence is used for the second and third virial coefficients and the conformai solution model is used for equation-of-state density terms beyond the third virial term. It is found that when values of unity are used for all binary and three-body unlike interaction parameters, calculated densities for methane-normal heptane mixtures have average absolute deviations of 3.54% for MDA, 4.04% for VDW1, and 2.59% for HMR. When vapor-liquid equilibrium calculations were performed for the methane-normal heptane system, average absolute deviations of calculatedK values from experimental values were 16.7% for methane and 36.4% for normal heptane using HMR, whereas when conformal solution model (CSM) mixing rules were used, the results were 34.8% for methane and 66.7% for normal heptane. When the binary interaction parameter for the characterization of interaction energies is determined, it is found to be less sensitive to state conditions in the case of HMR than either MDA or VDW1. These preliminary results suggest the potential of mixture equation-of-state methods which utilize rigorous composition dependence for the lower-order virial coefficients.
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    URL: http://dx.doi.org/10.1007/BF01133568
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    Densities of tetramethylsilane, tetraethylsilane, and tetraethoxysilane under high pressures (1990)
    Springer
    International journal of thermophysics 11 (1990), S. 477-486 
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    ISSN: 1572-9567
    Keywords: density ; equation of state ; high pressure ; Tait equation ; tetraethylsilane ; tetraethoxysilane ; tetramethylsilane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Accurate density data for tetramethylsilane, tetraethylsilane, and tetraethoxysilane in the temperature range from 283.15 to 333.15 K under pressure up to 100 MPa have been measured in order to test existing correlation methods. We have also measured the saturated liquid densities of tetramethylsilane, tetraethylsilane, and tetraethoxysilane in the temperature range from 283 to 343 K. The modified Rackett equation and the COSTAD correlation were used to correlate the saturated liquid density data. The Tait equation and a modified van der Waals equation of state were used to correlate the liquid density data under pressure. It was found that the average absolute deviations of the experimental values from those calculated with the Tait equation and the modified van der Waals equation of state were less than 0.01 and 0.21%, respectively. The effective hard sphere diameters for these three silane compounds were determined from the modified van der Waals equation of state parameter. It was found that the effective hard-sphere diameter decreases with temperature.
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    Thermodynamic properties of 1,1,1,2-tetrafluoroethane (R134a) in the critical region (1991)
    Springer
    International journal of thermophysics 12 (1991), S. 515-540 
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    ISSN: 1572-9567
    Keywords: critical phenomena ; equation of state ; R134a ; refrigerants ; sound velocity ; specific heat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A theoretically based simplified crossover model, which is capable of representing the thermodynamic properties of fluids in a large range of temperatures and densities around the critical point, is presented. The model is used to predict the thermodynamic properties of R134a in the critical region from a limited amount of available experimental information. Values for various thermodynamic properties of R134a at densities from 2 to 8 mol·L−1 and at temperatures from 365 to 450 K are presented.
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    Extension of thermophysical and thermodynamic property measurements by laser pulse heating up to 10,000 K. II. Under vacuum (1990)
    Springer
    International journal of thermophysics 11 (1990), S. 771-787 
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    ISSN: 1572-9567
    Keywords: charged particle emission ; emissivity ; equation of state ; evaporation ; gas dynamics ; high-speed photography ; high temperatures ; Knudsen technique ; Langmuir probe ; laser pulse heating ; mass spectrometry ; pyrometry ; thermionic emission ; transient heating ; work function ; vapor pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The experimental and theoretical efforts for the extension of thermodynamic property measurements up to 10,000 K by a transient-type dynamic laser pulse-heating technique under vacuum (LHV) are reviewed. The technique includes laser pulse heating, mass spectrometry, multiwavelength pyrometry, spectroscopy, high-speed photography, Langmuir probe, and high-tension diode studies. The experimental requirements and applicability limits of this transient technique at extreme rates of evaporation and charged particle emission under hydrodynamic flow conditions are discussed. Special attention is given to the study of the vaporization behavior and equation of state of multicomponent systems, the charged particle emission of ions and electrons, and the gas dynamic expansion mechanism of the evaporating jet. Further applications are the study of the reaction mechanism of combustion processes to investigate their efficiency and pollution.
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    Shell effects in the equation of state of metals (1992)
    Springer
    International journal of thermophysics 13 (1992), S. 315-329 
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    ISSN: 1572-9567
    Keywords: equation of state ; high pressures ; ionization ; quasiclassical approach ; Thomas-Fermi model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A simple quasiclassical Z-scaling model (QMT) is proposed to calculate the electron equation of state (EOS) for matter with a high energy concentration. This model may be employed over a wide range of densities and temperatures from the Saha model region of application to the corrected Thomas-Fermi model model (TFC) area of use. The treated model describes ab initio typical step behavior of the ionization state and energy as a result of successive shell ionization with increased temperature. The model naturally includes the effects of electron-ion interaction with increased density. This EOS model may be interesting for gas dynamics, energetics, astrophysics, etc.
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    A generalized process for phase equilibrium calculation with cubic equations of state (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 1101-1108 
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    ISSN: 1572-9567
    Keywords: equation of state ; fugacity ; phase equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper presents a general method for calculating the fugacity coefficient with a view to representing phase equilibria of fluids on the basis of cubic equations of state with two, three or four parameters. The basic formalism selected in this study is that of Schmidt and Wenzel.
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    Measurements of the virial coefficients and equation of state of the carbon dioxide+ethane system in the supercritical region (1992)
    Springer
    International journal of thermophysics 13 (1992), S. 1011-1032 
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    ISSN: 1572-9567
    Keywords: carbon dioxide ; densities ; equation of state ; ethane ; PρT ; mixtures ; virial coefficients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Gas-phase densities of the system carbon dioxide+ethane were measured with a Burnett apparatus at 320 K and at pressures up to approximately 10 MPa. Measurements were made on systems having carbon dioxide mole fractions of 0, 0.25166, 0.49245, 0.73978, and 1. Second and third virial coefficients were determined for each composition, and the cross virial coefficients were calculated. Comparisons were made with other recent high-quality measurements on this system. For each mixture compositionPρT measurements were made on five isochores having densities within ±30% of the critical density. Temperatures varied from 288 to 320 K. The two-phase boundary was determined and estimates are given forT c andP c for each composition.
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    An improved parametric crossover model for the thermodynamic properties of fluids in the critical region (1993)
    Springer
    International journal of thermophysics 14 (1993), S. 1-32 
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    ISSN: 1572-9567
    Keywords: critical phenomena ; equation of state ; ethane ; methane ; sound velocity ; specific heat ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An improved parametric equation for the thermodynamic properties of fluids is presented that incorporates the crossover from singular thermodynamic behavior in the immediate vicinity of the critical point to regular thermodynamic behavior far away from the critical point. Based on a comparison with experimental data for ethane and methane, it is demonstrated that the crossover model is capable of representing the thermodynamic properties of fluids in a large range of temperatures and densities around the critical point.
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    Equation-of-state measurements for crude oils at pressures up to 1 GPa (1993)
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    International journal of thermophysics 14 (1993), S. 215-220 
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    Keywords: bulk modulus ; compressibility ; crude oil ; equation of state ; high pressure
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    Notes: Abstract Equation-of-state measurements of two crude oils with different compositions and viscosity were performed at room temperature in the pressure range 0〈P〈1.0 GPa. We found large compressibilities and a strong dependence of the compressibility on oil content and viscosity. The bulk modulus changed with pressure from 2.0 to 12.1 GPa for one oil and from 1.3 to 9.5 GPa for the other. We discuss the possibility of detecting phase transitions in the region under investigation. The Tait and Murnaghan equations of state were fitted to the data, and residuals are presented.
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    The density of 1,1-dichloro-1-fluoroethane (HCFC 141b) (1994)
    Springer
    International journal of thermophysics 15 (1994), S. 375-377 
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    ISSN: 1572-9567
    Keywords: density ; 1,1-dichloro-1-fluoroethane ; equation of state ; HCFC 141b
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this Note we present the density of HCFC 141b, measured between 293.15 and 300.15 K, with an mechanical oscillator densimeter, with an uncertainty of 0.007%. The results are compared with the densities estimated by the reduced hard-sphere-DeSantis equation of state and with the experimental data obtained by several authors.
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    Equation of state for fluid alkali metals: Binodal (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 533-543 
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    ISSN: 1572-9567
    Keywords: alkali metals ; binodal ; corresponding states ; equation of state ; fluid metals ; rectilinear diameter ; thermodynamic similarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The three-parameter generalized van der Waals equation of state for liquids and gases is analyzed. This equation contains the generalized expressiona/V" for the molecular pressure: here the parametern takes into account the specificity of intermolecular attractive forces for various substances. The equation is presented in the reduced form, from which follows the single-parameter law of corresponding states with the thermodynamic similarity parametern. 11 is established that for alkali metals the value of the parameter it is the same and does not depend on temperature substantially. From the given generalized equation, the expressions for the binodal (equilibrium curve of the liquid and vapor phases) are obtained. For cesium. rubidium, and potassium, the temperature dependence of density is calculated over the temperature range from their melting point to the critical point: the results of the calculations agree with experimental data. It is established that for alkali metals, the law of rectilinear diameter breaks down in the vicinity of the critical point.
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    URL: http://dx.doi.org/10.1007/BF01441919
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    A thermodynamic property formulation for cyclohexane (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 519-531 
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    ISSN: 1572-9567
    Keywords: cyclohexane ; equation of state ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A formulation for the thermodynamic properties of cyclohexane is presented. The equation is valid for single-phase and saturation states from the melting line to 700 K at pressures up to 80 MPa. It includes a fundamental equation explicit in reduced Helmholtz energy with independent variables of reduced density and temperature. The functional form and coefficients of the ancillary equations were determined by weighted linear regression analyses of evaluated experimental data. An adaptive regression algorithm was used to determine the final equation. To ensure correct thermodynamic behavior of the Helmholtz energy surface the coefficients of the fundamental equation were determined with multiproperty fitting, Pressure-density-temperature (P-p-T) and isobaric heat capacity (C p -P-T) data were used to develop the fundamental equation, SaturationP-p-T values, calculated from the estimating functions, were used to ensure thermodynamic consistency at the vapor-liquid phase boundary. Separate functions were used for the vapor pressure, saturated liquid density, saturated vapor density. ideal-gas heat capacity. and pressure on the melting curve, Comparisons between experimental data and values calculated using the fundamental equation are given to verify the accuracy of the formulation. The formulation given here may be used to calculate densities within ±0.1 %, heat capacities to within ±2 %. and speed of sound to within ± 1 %, except near the critical point.
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    URL: http://dx.doi.org/10.1007/BF01441918
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    Vapor–Liquid Equilibrium of HFC-32/134a And HFC-125/134a Systems (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 519-530 
    Details
    ISSN: 1572-9567
    Keywords: activity coefficients ; binary interaction parameters ; equation of state ; fugacity coefficients ; HFC-32/134a mixture ; HFC-125/134a mixture ; thermodynamic consistency ; vapor–liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A vapor-liquid equilibrium apparatus has been developed and used to obtain data for the binary HFC-32/134a and HFC-125/134a systems. Twenty-two equilibrium data are obtained for the HFC-32/134a system over the temperature range from 258.15 to 283.15 K at 5 K intervals and the composition range from 0.2 to 0.8 liquid mole fraction. Twenty-five equilibrium data are obtained for the HFC-125/134a system over the temperature range from 263.15 to 303.15 K at 10 K intervals and the composition range from 0.18 to 0.81 liquid mole friction. These data have been tested and found to be thermodynamically consistent. Based upon the present data, the binary interaction parameters of the Carnahan-Starling-De Santis (CSD) and Redlich–Kwong–Soave (RKS) equations of state are calculated for five isotherms for the HFC-125/134a mixture and six isotherms for the HFC-32/134a mixture. The calculated results from the CSD equation are compared with data in the open literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022605104490
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    Equation of State for Complex Liquid Mixtures from Surface Tension (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 601-610 
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    ISSN: 1572-9567
    Keywords: complex liquid mixtures ; corresponding states ; equation of state ; surface tension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The present work shows a successful extension of previous studies to molecular liquids for which the second virial coefficients are not known. Recent advances in the statistical mechanical theory of equilibrium fluids can be used to obtain an equation of state (EOS) for compressed normal liquids and molten alkali metals. Three temperature-dependent quantities are needed to use the EOS: the second virial coefficient, B(T), an effective van der Waals covolume, b(T), and a scaling factor, α(T). The second virial coefficients are calculated from a correlation that uses the surface tension, γtr, and the liquid density at the triple point. Calculation of α(T) and b(T) follows by scaling. Thus, thermodynamic consistency is achieved by use of two scaling parameters (γtr, ρtr). The correlations embrace the temperature range T tr〈T〈T c and can be used in a predictive mode. The remaining constant parameter is best found empirically from ρtr data for pure dense liquids. The equation of state is tested on 42 liquid mixtures The results indicate that the liquid density at any pressure and temperature can be predicted within about 5%, over the range from T tr to T c.
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    URL: http://dx.doi.org/10.1023/A:1022613306307
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    A Generalized Model for the Thermodynamic Properties of Mixtures (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 825-835 
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    ISSN: 1572-9567
    Keywords: cryogens ; equation of state ; hydrocarbons ; mixtures ; refrigerants ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A mixture model explicit in Helmholtz energy has been developed which is capable of predicting thermodynamic properties of mixtures containing nitrogen, argon, oxygen, carbon dioxide, methane, ethane, propane, n-butane, i-butane, R-32, R-125, R-134a, and R-152a within the estimated accuracy of available experimental data. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single generalized equation which is applied to all mixtures studied in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures at various compositions including dew and bubble point properties and critical points. It incorporates accurate published equations of state for each pure fluid. The estimated accuracy of calculated properties is ±0.2% in density, ±0.1 % in the speed of sound at pressures below 10 MPa, ±0.5% in the speed of sound for pressures above 10 MPa, and ±1% in heat capacities. In the region from 250 to 350 K at pressures up to 30 MPa, calculated densities are within ±0.1 % for most gaseous phase mixtures. For binary mixtures where the critical point temperatures of the pure fluid constituents are within 100 K of each other, calculated bubble point pressures are generally accurate to within ±1 to 2%. For mixtures with critical points further apart, calculated bubble point pressures are generally accurate to within ±5 to 10%.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022627001338
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    Thermophysical Properties of Gaseous Tungsten Hexafluoride from Speed-of-Sound Measurements (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 185-206 
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    ISSN: 1572-9567
    Keywords: equation of state ; intermolecular potential ; speed-of-sound ; thermodynamic properties ; transport properties ; tungsten hexafluoride ; virial coefficients ; viscosity ; WF6
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The speed of sound was measured in gaseous WF6 using a highly precise acoustic resonance technique. The data span the temperature range from 290 to 420 K and the pressure range from 50 kPa to the lesser of 300 kPa or 80% of the sample's vapor pressure. At 360 K and higher temperatures, the data were corrected for a slow chemical reaction of the WF6 within the apparatus. The speed-of-sound data have a relative standard uncertainty of 0.005%. The data were analyzed to obtain the ideal-gas heat capacity as a function of the temperature with a relative standard uncertainty of 0.1%. These heat capacities are in reasonable agreement with those determined from spectroscopic data. The speed-of-sound data were fitted by virial equations of state to obtain the temperature dependent density virial coefficients. Two virial coefficient models were employed, one based on square-well intermolecular potentials and the second based on a hard-core Lennard–Jones intermolecular potential. The resulting virial equations reproduced the sound-speed data to within ±0.005% and may be used to calculate vapor densities with relative standard uncertainties of 0.1% or less. The hard-core Lennard–Jones potential was used to estimate the viscosity and the thermal conductivity of dilute WF6. The predicted viscosities agree with published data to within 5% and can be extrapolated reliably to higher temperatures.
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    URL: http://dx.doi.org/10.1023/A:1006617223481
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    Prediction of Critical Properties of Binary Mixtures Using the PRSV-2 Equation of State (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 239-258 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; critical properties ; equation of state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The aim of this work is to test the value of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state for predicting the critical behavior of binary mixtures. A procedure adopted by Heidemann and Khalil, based on the Helmholtz free energy, has been followed. The resulting two complex nonlinear equations have been solved simultaneously for the critical temperature and volume, while the critical pressure is calculated from the PRSV-2 equation of state itself. Three forms of binary-interaction parameters have been tried: the zero-type, conventional one-parameter type, and Margules two-parameter type. The optimum values of the binary interaction parameters, based on minimizing the sum of the squares of the relative errors between predicted and experimental critical temperatures, have been calculated for 20 polar and nonpolar systems. The Margules two-parameter type gives the best results, but its mathematical derivation is cumbersome and it requires more computation time. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperatures and pressures agree well with the experimental results, and are always better than those predicted by the group-contribution method. The deviations in the predicted critical volumes using any of the tested binary-interaction parameter types are relatively large compared to those using the group-contribution method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021463405545
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    Equation of State for Nonpolar Fluids: Prediction from Boiling Point Constants (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1123-1137 
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    ISSN: 1572-9567
    Keywords: compressed liquids ; corresponding states ; equation of state ; gases ; second virial coefficient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new corresponding states correlation for the second virial coefficient of nonpolar fluids in terms of the boiling point constants is presented. The scaling constants are the normal boiling point temperature, T bp, which is used to form a dimensionless temperature and the liquid density at the normal boiling point, ρ bp, which is used to form a dimensionless second virial coefficient. The procedure has been examined for a large number of substances including noble gases, diatomic molecules, saturated hydrocarbons up to C8, and a number of aliphatic, aromatic, and cyclic hydrocarbons. The resulting correlation has been applied to predict the equation of state of fluids over the range from the vapor-pressure curve to the freezing curve at various temperatures from the triple point up to the nonanalytical critical region. The equation of state has been applied to reproduce the liquid density of a great number of compounds both in the saturation and compressed states, at temperatures up to 2000 K and pressures up to 10000 bar, within an accuracy of a few percent. In particular we have shown that knowledge of two readily measurable constants is sufficient to determine the pvT surface of pure normal fluids having a variety of structural complexities.
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    URL: http://dx.doi.org/10.1023/A:1026498021221
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    Equation of state and critical point of cesium (1990)
    Springer
    International journal of thermophysics 11 (1990), S. 467-476 
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    ISSN: 1572-9567
    Keywords: cesium ; compressibility ; critical parameters ; density ; dilatometer ; equation of state ; high temperatures ; thermal expansion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Equation-of-state measurements for cesium at temperatures from 350 to 2200 K and pressures from 1 to 60 MPa by means of a hermetically sealed two-zone dilatometer are presented. The experimental range includes the liquid and gaseous phases together with the coexistence curve up to critical point and supercritical region. The critical parameters are 1938 K, 9.4 MPa, 0.39 g · cm−3. The data were used for the calculation of tables of the density and its derivatives for cesium. The results are discussed.
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    URL: http://dx.doi.org/10.1007/BF00500839
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    Cubic equations of state for transport properties (1991)
    Springer
    International journal of thermophysics 12 (1991), S. 333-356 
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    ISSN: 1572-9567
    Keywords: equation of state ; thermal conductivity ; transport equation of state ; viscosity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A method is presented for the prediction of the background contribution of residual thermal conductivities and residual viscosities of nonpolar or slightly polar substances. The method is based on the concept of transport equations of state describing the transport properties in terms of pressure and temperature by pressure explicit equations similar to thermal equations of state. The transport equation of state is derived from a generalized cubic thermal equation of state and a universal function for the density dependence of the residual part of the transport properties. A comparison of calculated and recommended values of the thermal conductivity of 35 and the viscosity of 23 substances yields an absolute average deviation of 6% for the thermal conductivity and of 5% for the viscosity. The Maxwell condition is applied to the generalized transport equation of state to predict consistently the transport properties along the vapor-liquid coexistence curve.
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    URL: http://dx.doi.org/10.1007/BF00500756
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    Thermodynamic properties of methane in the critical region (1992)
    Springer
    International journal of thermophysics 13 (1992), S. 671-684 
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    ISSN: 1572-9567
    Keywords: coexistence curve ; critical phenomena ; equation of state ; methane ; sound velocity ; specific heat ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An equation of state is presented for the thermodynamic properties of methane in the vicinity of the critical point. It incorporates the scaled asymptotic critical behavior predicted theoretically and supplements a global analytic equation of state for methane recently developed by Setzmann and Wagner.
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    URL: http://dx.doi.org/10.1007/BF00501948
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    Measurement and prediction of ultrasonic speed under high pressure in natural gases (1994)
    Springer
    International journal of thermophysics 15 (1994), S. 803-819 
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    ISSN: 1572-9567
    Keywords: equation of state ; high pressure ; natural gas ; ultrasonic speed
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Ultrasonic-speed measurements have been performed on two natural gases with significantly different compositions. The systems have been investigated from 12 to 70 MPa in the temperature domain from 263 to 413 K. Furthermore, the ultrasonic-speed data obtained are compared with the values predicted by means of various equations of state.
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    URL: http://dx.doi.org/10.1007/BF01447096
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    Describing vapor-liquid equilibria in methanol +n-alkane systems by means of an equation of state with association (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 227-236 
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    ISSN: 1572-9567
    Keywords: association ; equation of state ; false liquid-liquid split ; methanol +n-alkane systems ; mixing rule ; vapor-liquid equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The ability of an equation of state incorporating association to describe vapor-liquid equilibrium of methanol +n-alkane systems has been tested. An equation of state with association is divided into “physical” and “chemical” parts, where the Patel-Teja cubic equation of state is used for the description of the physical part and an association tenn forms the chemical part. Five two- and threeparameter mixing rules were tested and compared with an equation of state without association. On the average for the first eight n-alkanes, the improvement in fit of pressure using association was 30–50 % and the calculated vapor compositions were also much improved. In addition, there were lewer points with unstable liquid phase (false liquid-liquid split). Both with and without association, density-dependent mixing rules based on a local-composition concept gave the best result.
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    URL: http://dx.doi.org/10.1007/BF01438973
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    The selection of international standards for the thermodynamic properties of HFC-134a and HCFC-123 (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 781-790 
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    ISSN: 1572-9567
    Keywords: environmentally acceptable refrigerants ; equation of state ; thermodynamic properties ; international standards
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The objectives and activities of the International Energy Agency-Annex 18 are summarized. One of the goals of the Annex was to determine the formulations that best represent the thermodynamic properties of HFC-134a and HCFC-123. The formulations selected were those which accurately represented the experimental data and simultaneously exhibited thermodynamic consistency. Methods of comparison include analysis of the experimental data, statistical comparisons of values calculated from the property formulations to experimental values, and graphical analyses of the thermodynamic surface. The analytical methods used are summarized in this paper. The equations of state reviewed in these comparisons represented the most accurate formulations available in December 1992. Four equations of state were reviewed for HFC-I34a and three equations of state were considered for HCFC-123. These equations represented the work of independent researchers in Germany, Japan, and the United States. The formulations selected as international standards are presented.
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    URL: http://dx.doi.org/10.1007/BF01438863
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    Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 563-588 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; critical region ; D2O ; equation of state ; H2O ; phase behavior ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A parametric crossover model is adapted to represent the thermodynamic properties of pure D2O in the extended critical region. The crossover equation of state for D2O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D2O + H2O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D2O and for the D2O + H2O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T c(x)≤T≤1.5T c(x) and densities 0.35ρc(x)≤ρ≤1.65ρc(x).
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    URL: http://dx.doi.org/10.1023/A:1022609205399
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    The Equation of State of Song and Mason Applied to Fluorine (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 611-629 
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    ISSN: 1572-9567
    Keywords: equation of state ; fluorine ; thermodynamic properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An analytical equation of state is applied to calculate the compressed and saturation thermodynamic properties of fluorine. The equation of state is that of Song and Mason. It is based on a statistical–mechanical perturbation theory of hard convex bodies and is a fifth-order polynomial in the density. There exist three temperature-dependent parameters: the second virial coefficient, an effective molecular volume, and a scaling factor for the average contact pair distribution function of hard convex bodies. The temperature-dependent parameters can be calculated if the intermolecular pair potential is known. However, the equation is usable with much less input than the full intermolecular potential, since the scaling factor and effective volume are nearly universal functions when expressed in suitable reduced units. The equation of state has been applied to calculate thermodynamic parameters including the critical constants, the vapor pressure curve, the compressibility factor, the fugacity coefficient, the enthalpy, the entropy, the heat capacity at constant pressure, the ratio of heat capacities, the Joule–Thomson coefficient, the Joule–Thomson inversion curve, and the speed of sound for fluorine. The agreement with experiment is good.
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    URL: http://dx.doi.org/10.1023/A:1022665323146
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